Maximizing solar radiations of PV panels using artificial gorilla troops reinforced by experimental investigations

doi:10.21203/rs.3.rs-3213784/v1

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Maximizing solar radiations of PV panels using artificial gorilla troops reinforced by experimental investigations

https://doi.org/10.21203/rs.3.rs-3213784/v1

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published 12 Feb, 2024

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The aim of this work is to maximize the solar radiations (SRs) by computing the optimal tilt angle (OTA) of photovoltaic (PV) panels by using gorilla troop algorithm (GTA) along with an experimental work that consists of three PV panels rated 100 W inclined at three different tilt angles (TAs). The three TAs are 28^o, 30^o, and 50^o. These TAs are selected based on experience and after huge simulations and physical trials. The experimental data are recorded daily for a period of 181 days and the data showed that the TA of 28^o is better than that at 50^o and 30. The GTA computed the OTA as 28.445^o which is in agree with that obtained from the experimental investigations that has a TA of 28^o. The SR of the 28^o TA is higher than that of the 50^o TA by 59.3% and better than the TA of 30^o by 4.5%. For the sake of comparison with the GTA with other 8 metaheuristic (MHTs) recent techniques are used to find the best OTA. Most of the 8 MHTs computed the OTA as 28.445^o which is the same as computed from the GTA and matches that obtained from the experimental work has a value of 28^o. The experimental recorded SR difference between the 28^o TA and the 50^o TA was 159.3% in only 181 days which signifies the importance of having correct TA for the PV tracker.

Physical sciences/Engineering/Electrical and electronic engineering

Physical sciences/Energy science and technology/Energy harvesting

Optimum tilt angle

Renewable energy

Solar radiations

PV panels

Metaheuristic techniques

Artificial gorilla troop algorithm

Solar energy utilization by PV has become a vital source of renewable energy (RE) [1]. There are many factors affecting the performance of the PV system. The tilt angle (TA) of solar panels is one of these factors which can effectively enhance the electrical energy production. In the last five years, numerous researches have been conducted in various countries around the world to determine the OTA for solar panels [2].

These studies have used various techniques and software to compute the OTA. These include mathematical modeling and numerical simulations, experimental approaches, and Artificial Intelligence (AI)-based methods. Also, these studies nearly covered most of the world countries such as China, Spain, India, Brazil, Turkey, Algeria, Iraq, Malaysia, Pakistan, Saudi Arabia, Iran, Morocco, Libya, Egypt, Ecuador, Ethiopia, and Uganda. For instance, in Turkey [3], Cagman found that PV panels tilted at a 30° angle at Bursa city that has latitude angle (LA) of 40.1885° N generates more energy than that is tilted at 13° by 42.17 kWh/year or 2.45%, with CO2 production discount of 495 tons for a period of twenty five years. This is agreed with that the TA is very near to the Oulimar, and Bellaoui [4] implemented a study to find the OTA in Adrar, Algeria that has LA of 27.874° N. The study was based on collecting data for eleven years. The outcomes of the study stated that the OTA is 28°, which is very near to the LA.

In [5], Ponce-Jara and Rus-Casas suggested the use of a tracking system for PV to improve the efficiency of the PV panels in Ecuador. The authors of the current study believe that a tracker system is not suitable for PV panels from the practical point of view. A remarkable work was done in Brazil by Cavalcanti and Batista [6] in which a comparison has been made between three PV systems which were installed in the state of Ceará, Brazil which has LA of -3.731862^o. The first and second systems are fixed at TAs of 18^o and 22^o and the third system has a solar tracker. The total cost of the three systems were 1428.47$, 1428.57$ and 1921.43$ respectively. The system with TA of 18^o has the lowest performance, and the system with TA 22^o has a performance very near to that with solar tracker but with lesser costs but without the extra cost of the tracker.

Memon and others in [7, 8] presented a numerical analysis using MATLAB/Simulink to find the OTA for a 1 MW PV system that was previously installed at 15^o TA at Sukkur IBA university in Pakistan that has latitude of 27.73^o N. The OTA was found to be 29.5^o. Although is OTA is very near to the LA, but the authors of the current study are sure that the OTA is slightly less that the LA. Xu a and Longin [9] investigated the OTA for areas with high elevation in Batang County, Sichuan, and China that has latitude 30.0054° N. They used a TA of 40^o for best performance. In [10], a comparison between two TAs is implemented in Kelantan, Malaysia. The first TA is 40^o and the other panel is horizontal. The TA of 40^o had better performance than the horizontal surface, which is logical sine the horizontal surface is very far from the LA. A thorough study has been implemented in [11] to find the OTA for different cities in Iraq. The study used a data that were collected in 19 years and suggested that the TAs for winter months are different from those for summer months. The study ended by suggesting an annual OTA for 18 cities in Iraq.

In [12], a study has been made to find the annual OTA for Yazd city in Iran (Latitude 31.54^o) and it was found to be 29.38^o, which is convenient since it is slightly less than the Ashetehe [13] computed the seasonal and yearly OTAs for Bahir Dar city (Latitude 11.5742° N) in Ethiopia. Yadav [14] suggested that there is a link between OTA and the LA which is stated by many other authors. Mamun, et al. in [15] suggested a 15^o is the best TA for all cities in Malaysia (LA 4.2105° N). Similar work was done in [16] in Punjab, Pakistan which has LA of 31.1471° N but suggested the same TA of 15^o which far from the value of the Karinka and Upadhyaya [17] stated that if the PV panels are not tilted at monthly OTA, there will be an energy loss of 12%. Morad and Al-Sayyab [18] a study had been implemented compute the annually and monthly OTA at three cities in Iraq. These cities are the capital which has LA of 33.33°, Tikrit that has LA of 34.58°, and Diyala which has LA of 33.233°. The authors suggested that one OTA of 31 for the three cities. Tamoor and Habib [19] a studied has been implemented in Pakistan suggested that a TA of 15^o is acceptable for PV panels. Obiwulu and Erusiafe in [20] used 6 systems tilted at different TAs in Nigeria, and suggested that a TA of 16.8^o gives the best performance. Ashetehe [21] continued his work made in [13] and suggested OTA for some cities in Ethiopia. The OTAs were computed in some cities in SA in by Mansour [22] and he suggested that for the city of Riyadh that has LA of 24.7136° N, a TA of 22.7 was chosen to be the best TA.

Farahat [23] selected TAs of 30°, 20° and 25° for some cities in SA. Sharma [24] suggested the monthly OTA for Pradesh, India that has LA of 31.7° N. Sahin [25] used ANN to compute the OTA in Turkey and stated that the OTA can rise SR by 34%. Taha and Hameed [26] computed the OTA in Duhok University that has LA of 36.862^o and it its value was 32.7^o. Nfaoui [27] computed the OTA that gives the optimal SR in Morocco. Abdelaal and et al. [28] conducted through simulations to determine the OTA for each day, each month, each season, and for the whole year. They computed the OTA in some cities in EGYPT. Similar works can be found in references [1, 2, 29–41] which they focused on the computation of the OTA that gives the optimal SR in different countries.

Recently heuristics methods have been used to get the OTA. For example in [42], the Particle Swarm Optimizer (PSO) and Bee colony (BC) were used to calculate the OTA. The results shows that a very slight difference between the two methods. Most of the pervious methods showed that the OTA is very near to the LA and the difference between the two computed angles in the range of 1 to 3 degrees.

This work is focused on estimating the OTA by GTA, beside with an experimental work on three PV tilted systems. Also other MHT were used to compare the results with that obtained from GTA.

The main contributions of the present work are i) firstly is to explain the significance of the TA that gives nearly a constant SR all over the year, otherwise money lost will results in, ii) The use of GTA and other 8 MHTs to compute the OTA, and iii) The results are verified by an experimental work done by using 3 PV panels placed at 3 different tilt angles.

This paper is sorted as follow; the first section of the paper displays the previous work done in the computation of the OTA. Section 2 reviews the basic relations of SR on both horizontal and tilted surfaces. Section 3 analyzes the importance of the correct TA that gives a nearly constant SR all the year. Section 4 investigates the application of the GTA beside with 8 different MHTs to compute OTA. The 8 MHTs are genetic algorithms (GA), Particle Swarm (PS), Harmony Search (HS), Ant colony (AC), Cuckoo Search (CS), Bees Colony (BC), Fire Fly (FF), and Grey Wolf (GW). Section 5 shows the simulation results of these different techniques. The final section presents the experimental work that has been implemented on 3 different TAs.

The Mathematical model of SR can be described by the following equations [43]:

First the square of the inverse of the distance between sun and earth can be calculated from

$${\text{E}}_{o}={\left(\frac{{\text{d}}_{o}}{\text{d}}\right)}^{2}=1.00011+3.4221.1{0}^{-2}\text{c}\text{o}\text{s}\text{ϵ}+1.28.1{0}^{-3}\text{s}\text{i}\text{n} \text{ϵ}+7.19.1{0}^{-4}\text{c}\text{o}\text{s} 2\text{ϵ} +7.7\text{*}1{0}^{-5}\text{sin}2\in$$

where $\text{ϵ}$ is the angle of the day calculated from the following equation:

$$ϵ=\raisebox{1ex}{$2\pi \left(n-1\right)$}\!\left/ \!\raisebox{-1ex}{$365$}\right.$$

The declination angle δ can be calculated from

$${\delta }=\left(\text{6.918.1}{0}^{-3}-0.399912\text{cos}\text{ϵ}+7.0257.1{0}^{-2}\text{sin}\text{ϵ}-6.758.1{0}^{-3}\text{cos}2\text{ϵ}+ 9.07.1{0}^{-4}\text{sin}2\text{ϵ}- 2.697.1{0}^{-3}\text{cos}3\text{ϵ}+ 1.48.1{0}^{-3}\text{sin}3\text{ϵ}\right).\left(\frac{180}{\pi }\right)$$

The angle of the sun set with respect to a horizontal surface ${{\omega }}_{\text{s}}$ is calculated as

$${{\omega }}_{\text{s}}={\text{cos}}^{-1} (-\text{tan}{\phi }.\text{tan}{\delta }) \text{i}\text{n} \text{d}\text{e}\text{g}\text{r}\text{e}\text{e}\text{s}$$

where the angle φ is the latitude angle. The sun set hour angle of an inclined surface ${{\omega }}_{\text{s}}^{{\prime }}$ at a TA β is calculated as

$${{\omega }}_{\text{s}}^{{\prime }}=\text{m}\text{i}\text{n} \left\{{{\omega }}_{\text{s}}, \text{c}\text{o}{\text{s}}^{-1} \left[-\text{t}\text{a}\text{n} {\delta } \text{t}\text{a}\text{n} \left({\phi }-{\beta }\right)\right]\right\}$$

The SR at horizontal surface H_o is

$${\text{H}}_{\text{o}}=\frac{24}{{\pi }}.{\text{I}}_{\text{S}\text{C}}.{\text{E}}_{\text{o}}.\text{cos}{\delta }.\text{ cos}{\phi }.[\text{sin}{{\omega }}_{\text{s}}-({\pi }/180\left){{\omega }}_{\text{s}}\text{cos}{{\omega }}_{\text{s}}\right]$$

While The SR on inclined surface H_oβ is

$${\text{H}}_{\text{o}{\beta }}=\frac{24}{{\pi }}.SC.{\text{E}}_{\text{o}}\left[ \frac{{\pi }}{180}\text{ }{{\omega }}_{\text{s}}^{{\prime }}\text{s}\text{i}\text{n} {\delta }.\text{sin}\left({\phi }-{\beta }\right)+\text{cos}{\delta }.\text{cos}\left({\phi }-{\beta }\right).\text{sin}{{\omega }}_{\text{s}}^{{\prime }}\right]$$

where SC is the solar constant. Equations (1)-(7) represent the complete system for estimating the SR at horizontal surface or inclined surface at an angle β.

In order to show the effects of the TA on the SR, Eqs. (1)-(7) are simulated using MATLAB for different TAs and their SR are shown in Fig. 1. The blue curve is drawn for a TA of 30^o which is very close to the LA of the Suez city. This curve shows that the SR varies slowly all over the year and the maximum value of SR is 10.5696 kWh/m²/day and the minimum value is 9.2192 kWh/m²/day difference between maximum and minimum values is 1.3504 kWh/m²/day or 14.65%.

As the TA goes away from the LA, the difference between the maximum and minimum becomes higher. For example for a TA of 50^o, the maximum value of the SR is 11.765 kWh/m²/day while the minimum value is 6.5941 kWh/m²/day. The difference between maximum and minimum values in this case is 5.1708 kWh/m²/day or 78.4158% of the minimum value which is too high and not acceptable from costs point of view since this can leads to waste money during the days of low SR. On the other hand if the TA is zero as for a horizontal surface, the maximum value of the SR is 11.4243 kWh/m²/day and the minimum value is 5.5511 kWh/m²/day. With a difference between the two values of 5.1708 kWh/m²/day or 105.8% of the minimum value which is also not acceptable for economic reasons as mentioned before. So one can state that when the TA is near the LA, the difference between the minimum and maximum value of the SR curve becomes smaller as shown from Fig. 1. When the TA departs away from the LA the difference between the minimum and maximum value of the SR curve becomes higher as shown from Fig. 1and money waste occurs at these TAs.

Figure 2 shows the SR for 3 close TAs, which are 28^o, 30^o, and 32^o. As shown from the figure, as we go above the LA, the characteristics of the SR diverge, and the difference between maximum and minimum values increases. Vice versa as the TA becomes close from the LA, the difference between maximum and minimum angles decreases. As we stated before the best TA has minimum value between maximum and minimum value. According to this the best TA in Fig. 2 is 28^o.

MHTs have appeared as great optimization methods [44–50]. Currently there are more than 500 MHTs are used in optimization [48]. Since MHTs are characterized by flexibility, adaptively and have excessive search capability, they found wide spread in different applications.

Although GA was the first MH method introduced by Holland [47], GA is still the most used optimization method as mentioned in a survey in[44, 45, 47, 48, 50]. A good review on GA is presented in [49]. There are three important parameters affecting the operation of GA. These parameters are crossover probability, mutation probability and size of the population. The GA is a simple, requires less data and efficient technique for solving optimization problems [49]. The PS [46] is developed and because of its simplicity, it is considered as the second wide spread used method in optimization [48]. The parameters used in PS are the particles location and their velocity. PS needs a smaller parameters to be tuned and has good convergence. The HS method has less computation efforts and is easy to implement [51]. The main parameters affecting the operation of HS are distance of the bandwidth, size of memory; rate of pitch adjustment, and choosing from memory rate. AC and BC [45, 52] are MHTs which are inspired by the social behavior of both ants and bees. The main parameters used in AC are the evaporation and weighting of pheromone. In CS [53], there are lesser parameters to be tuned and based on levy flight. CS can be very efficient in finding global solution. FF [54] was inspired by the blinking process of fireflies and is used wildly in different applications. The main parameter in the FF algorithm is the brightness of FF. Recently, the GW [55, 56] which imitates the hunting process of gray wolves. Recently the GTA [57] got a wide interest in many applications because of its superior convergence and it will be discussed in more details in the next section.

4.1 Artificial Gorilla Troops Algorithm

Like any society, Gorillas have sensitive state, have solid family ties, hunt for their own food and have a view about their past and future. Their foods fluctuate from one gorilla type to other types. Gorillas live in highlands, are mostly vegetarian. The leader of the group is called Silverback (SB) and he is the pivot of a group and he is in charge of many responsibilities like leading, searching and protecting of the group individuals. A good review about social behavior of GTA can be found in [57].

4.2 Procedures of the GTA

There are two phases that mimic the GTA behavior. The first phase is called exploration phase (EXP), and the second phase is the exploitations phase (EXTP). In the EXP, there are three places that a gorilla could migrate to it according to Eq. (8). The first one is to go unknown place when the migration probability parameter p is greater than a random number, the second is to go to known place when the random number is greater than or equal to 0.5. The third one is to go to other gorilla when the random number is less than 0.5. The parameter p should be specified at the beginning of the optimization process.

$$GX\left(IT+1\right)=\left\{\begin{array}{c}\left(Upp\_B-L\_B\right)*{r}_{1}+L\_B rand<p\\ \left({r}_{2}-C\right)\times {X}_{r}\left(IT\right)+L\times H rand\ge 0.5\\ X\left(k\right)-L\times \left(L\times \left(X\left(IT\right)-G{X}_{r}\left(IT\right)\right)+{r}_{3}\times \left(X\left(IT\right)-G{X}_{r}\left(IT\right)\right)\right) rand<0.5\end{array}\right.$$

In Eq. (8), Upp_B is the upper bound of the designing variables, and L_B is the lower bound and rand, r₁, r₂, r₃ and rand are random numbers. The value of C, L and H can be determined by Eqs. (9)-(13). X denotes the position of the gorilla, ${X}_{r}$ is a randomly chosen gorilla, X(IT) is the position of the gorilla at iteration number IT, X(k) gorilla number k, and GX(IT + 1) is the new position of the gorilla at iteration (IT + 1).

$C=F\times \left(1-\frac{IT}{Max\_IT}\right)$	(9)
$F=\text{cos}\left(2\times {r}_{4}\right)+1$	(10)
$L=C\times l$	(11)
$H=Y*X\left(IT\right)$	(12)

where r₄ and l are random numbers and Y is a random number limited between - C to C or

$$Y = [-C, C]$$

On the other hand, there are two processes in the EXTP. The first one is to follow the SB when C ≥ W. These can be described by Eqs. (14)-(16).

$$GX\left(IT+1\right)=L*M*\left[X\left(IT\right)- {X}_{silverback}\right]+X\left(IT\right)$$

where L is calculated as in Eq. (10) and M is given as

$$M= {\left[{\left|\frac{1}{{N}_{pop}} \sum _{j=1}^{{N}_{pop}}G{X}_{j}\left(IT\right)\right|}^{g}\right]}^{\left(\frac{1}{g}\right)}$$

$$g= {2}^{L}$$

where ${\text{X}}_{\text{s}\text{i}\text{l}\text{v}\text{e}\text{r}\text{b}\text{a}\text{c}\text{k}}$ is the silverback position.

The other process is to contest for adult female when C < W, which can be described by Eqs. (17)-(20).

$GX\left(k\right)={X}_{silverback}-\left[ {X}_{silverback}Q-X\left(IT\right)Q\right]+X\left(IT\right)]*A$	(17)
$Q=2* {r}_{5}-1$	(18)
$A= \beta *E$	(19)
$E= \left\{\begin{array}{c}{N}_{1} rand \ge 0.5 \\ {N}_{2} rand<0.5 \end{array}\right.$	(20)

The complete flow chart showing the GTA is shown in Fig. 3.

The GTA algorithm is implemented using MATLAB to find the OTA, and the results are investigated in the next portion.

The key objective is to find the OTA for PV panels that gives the maximum SR. The optimization problem can be written in the following form:

Objective function (OF) is adapted to maximize the SR on a tilted surface by an angle λ, described by

$${\text{H}}_{\text{o}{\beta }}=\frac{24}{{\pi }}*SC*{\text{E}}_{\text{o}}\left[ \frac{{\pi }}{180}\text{ }{{\omega }}_{\text{s}}^{{\prime }}\text{s}\text{i}\text{n} {\delta }.\text{sin}\left({\phi }-{\beta }\right)+\text{cos}{\delta }.\text{cos}\left({\phi }-{\beta }\right).\text{sin}{{\omega }}_{\text{s}}^{{\prime }}\right]$$

The SR is subjected to the constraints depicted in Eqs. (1)-(6).

All variable names and their definitions are mentioned in Section 2. The objective is to use GTA to solve the OTA problem defined by Eq. (21).

The previous optimization problem has been simulated in MATLAB using the GTA. The different parameters in GTA used in simulation are given as follows: Population Size, N_pop = 30, maximum number of iteration, Max_IT = 50, number of designing variables = 1, lower bound, L_B =${0}^{o}$ and Upper bound, UPP_B = ${90}^{o}$ and The migration probability parameters with p = 0.03, β = 3 and w = 0.8. It may be good to mention that these adapted settings are cropped using trails and errors methodology to have better performance of the employed optimizer. Table 1 announces the key parameters of the 8 previously mentioned challenging methods.

Table 1

The main adapted parameters of the 8 MHTs
Method	Main Parameters	Method	Main Parameters
GA	Number of population = 50 Number of generations = 20 Number of elitism children = 2	CS	Number of nests = 100 Discovery rate of alien eggs = 0.25 Levy exponent and coefficient = beta = 3/2;
PS	Swarm Size = 50 Inertia Weight = 1 Inertia Weight Damping Ratio = 0.99 Personal Learning Coefficient = 1.5 Global Learning Coefficient = 2	BC	Population Size = 100 Number of Onlooker Bees = 100 Acceleration Coefficient Upper Bound = 1
HS	Harmony Memory Size = 50 Number of New Harmonies = 20 Harmony Memory Consideration Rate = 0.9 Pitch Adjustment Rate = 0.1 Fret Width Damp Ratio = 0.995	FF	Number of Fireflies = 100 Light Absorption Coefficient = 1 Attraction Coefficient Base Value = 2 Mutation Coefficient = 0.2 Mutation Coefficient Damping Ratio = 0.98
AC	Number of Ants = 100 Pheromone Exponential Weight = 0.3 Evaporation Rate = 0.1 number of divisions = 90	GW	Number of search agents = 24 The parameter a The coefficient vectors A and C

The convergence trend of the GTA is shown in Fig. 4 which shows the values of the OF (multiplied by -1 for maximization purpose) versus the iteration number. The AC and HS have the worst convergence process at the first few iterations. The remaining MHTs including GTA have similar convergence characteristics. In order to discriminate between these remaining MHTs, Fig. 5 shows the first 3 iterations. The horizontal black line represent 6 MHTs that have nearly same characteristics, and cannot differentiate between them. The 6 MHTs are BC, FF, CS, PS, GW, and GTA.

The OTA for some cities around the world are obtained from these MHTs and are shown in Table 3. Also the SR in kWh/m²/year is calculated for each OTA. The results are shown in Table 3 which shows the OTA and SR obtained by each methods.

The OTA of Suez city was calculated in [28] to be 28^o and was calculated in the previous section by GTA as 28.445^o but the MHTs identify the OTA to be 28.446^o. A slightly different solution is found by AC which gives an OTA of 28.507^o and yearly SR of 3630.6 kWh/m² which is nearly equal to the SR calculated from other methods. For the sake of comparison the OTAs for some other cities in other countries are calculated. For example the OTA for Madinah city in SA is reported in [58] as 23.5^o, but as shown in Table 1 by using MH methods, the OTA of Madinah is 23.3^o which gives a SR of 3640 kWh/m²/year. For the Mecca city, the OTA is calculated as 20.34^o. In [59], the OTA of Doha, Qatar, was estimated to be 25^o, but using MH methods give OTA of 24^o. For Dubai city, the OTA was calculated in Ref. [60] as 23.39^o but using MH algorithms the corrected OTA of Dubai city is 23.9 ^o which gives better SR.

Table 2 shows the OTA of some cities in different countries including Suez city in Egypt calculated using GTA and the other 8 methods.

Table 2

Yearly SR in kWh/m²/year at OTA
Method	Suez LA 29.9989^o N		Mecca (SA) LA 21.3891° N		Madinah (SA) LA 24.5247° N		Doha (Qatar) LA 25.2854° N		Dubai (UEA) LA 25.2048° N
	SR	OTA	SR	OTA	SR	OTA	SR	OTA	SR	OTA
GA	3630.596	28.446	3644.6	20.34	3640.4	23.3	3639.2	24.0	3639.3	23.9
PS	3630.596	28.445	3644.6	20.34	3640.4	23.3	3639.2	24.0	3639.3	23.9
HS	3630.600	28.446	3644.6	20.18	3640.4	23.2	3639.2	24.0	3639.3	23.8
AC	3630.600	28.507	3643.3	18.76	3638.7	21.5	3638.4	25.3	3638.4	25.3
BC	3630.596	28.445	3644.6	20.35	3640.4	23.3	3639.2	24.0	3639.3	23.9
FF	3630.596	28.12	3644.6	20.69	3640.4	23.8	3639.2	23.6	3639.3	24.1
CS	3630.596	28.445	3644.6	20.14	3640.4	23.3	3639.1	23.6	3639.3	23.9
GW	3630.596	28.445	3644.6	20.34	3640.4	23.3	3639.2	24.0	3639.3	23.9
GTA	3630.596	28.445	3644.6	20.34	3640.4	23.3	3639.2	24.0	3639.3	23.9

In order to compare the results obtained from all the nine methods, there many aspect can be taken into consideration but here we will consider firstly the accurate results, Technique complexity, CPU processing time, and also a parametric test will be performed on these MHTs. The independent runs are implemented on a PC with an Intel i7 4970 CPU processer running at 3.6 GHz. It is clear that the GTA, has the best accurate results, and the AC has the worst results this is clear from Fig. 5. Other method are close to the GTA, but the GTA is the best.

7.1 CPU processing time

In order to compare between the different from the CPU processing time, each technique has been run and its computation time is recorded, the results are shown in Table 3. From Table 3, one can see, that the GTA has the lowest CPU time which is 3.506, and the AC has the longest CPU time.

Table 3

CPU processing time
Method	GTA	GW	AC	HS	BC	FF	PS	CS	GA
CPU Time Sec.	3.506	3.981	1073.6	7 .223	9.573	225.28	5.075	8.243	13.888

7.2 Parametric tests

Parametric tests are statistical tests that suggest the data nearly tracks a normal distribution. In order to perform the parametric test, each method is implemented for 20 times, and each time the OTA is recorded. The results are shown in Table 4. Although all methods have a very small P value As shown from the last raw and the GTA has the lowest P-value.

Table 4

The values of the OTA against run number for each method
Run #	GTA	GW	AC	HS	BC	FF	PS
1	28.4450	28.4453	28.0068	28.4413	28.4453	28.4651	28.4450
2	28.4450	28.444	28.0069	28.4444	28.4419	28.3966	28.4450
3	28.4427	28.4451	28.0069	28.4441	28.4437	28.4424	28.4450
4	28.4450	28.446	28.0067	28.4461	28.4444	28.3747	28.4450
5	28.4447	28.445	28.0069	28.4451	28.4450	28.4157	28.4447
6	28.4452	28.4481	28.0069	28.4461	28.4449	28.4424	28.4452
7	28.4446	28.4447	28.5068	28.4554	28.4458	28.3747	28.4414
8	28.4450	28.445	28.5068	28.4436	28.4450	8.4221	28.4450
9	28.4451	28.4446	28.0069	28.4451	28.4453	28.4328	28.4450
10	28.4450	28.4449	28.0069	28.4421	28.4450	28.4451	28.4451
The P-value	1.385*10^− 5	0.0069	1.267*10^− 4	0.0041	0.0098	1.456*10^− 5	3.864*10^− 5

The P-value of the GTA is the lowest while the BC is the highest, although all methods have P-value that is lesser than 0.05

To verify the theoretical work, an experimental work consists of three PV panels were assembled at Suez University, that has latitude of 30°. The PV panels were directed towards the south and has different TAs of 28°, 30^o and 50°. Each PV system consists of one hundred watts PV panel, a peak power point tracker, a DC-AC converter, a storage battery, and an electrical load. There are two panels from these were used last year in [28], but the measurements were reported only for 60 days. In the present work, measurements were recorder for a period of 181 days, starting from Saturday 24th of December 2022, and ending on Saturday 24th June 2023. The complete system is shown in Fig. 6. The measurements are shown in Table 5. The data is given in Table 2 and is drawn in Fig. 7. From this figure, one can see that the TA of 28^o has the best performance. The SR of TA 28^o is better than the SR of TA 50^o by 59.3% and better than the TA of 30^o by 4.5%. It should be noted that these results not for all the year but only for 181 days.

Table 5

SR for the different experimental TAs in kWh
Day		TA			Day	TA			Day	TA			Day	TA
Day		28^o	30^o	50^o	Day	28^o	30^o	50^o	Day	28^o	30^o	50^o	Day	28^o	30^o	50^o
1		0	0	0.2	48	6.9	7.1	4.0	93	13.9	15.3	7.9	143	22.5	24.1	13.5
2		0.2	0.2	0.3	50	7.1	7.2	4	94	14.1	15.5	8.1	144	22.6	24.2	13.6
3		0.4	0.3	0.4	51	7.3	7.4	4.1	95	14.3	15.7	8.2	146	22.9	24.2	13.6
4		0.5	0.4	0.5	53	7.6	7.7	4.2	96	14.6	16.0	8.3	147	23.1	24.2	13.8
5		0.6	0.5	0.6	54	7.7	7.8	4.3	97	14.7	16.1	8.4	148	23.2	24.2	13.9
6		0.8	0.7	0.8	55	7.8	8.0	4.4	98	15.1	16.5	8.5	149	23.4	24.2	14.0
8		1.2	1.2	1.0	57	8.1	8.4	4.5	99	15.3	16.7	8.6	150	23.6	24.2	14.1
9		1.4	1.4	1.1	58	8.2	8.5	4.6	100	14.6	16.0	8.7	151	23.7	24.2	14.3
10		1.6	1.6	1.2	59	8.3	8.7	4.7	101	15.7	17.1	8.8	153	23.8	24.3	14.4
11		1.8	1.8	1.3	60	8.4	8.9	4.8	102	16.0	17.3	8.9	154	23.9	24.3	14.5
12		1.9	2.1	1.4	61	8.5	9.1	4.9	103	16.1	17.4	9.0	155	24.1	24.3	14.6
13		2.0	2.2	1.5	62	8.6	9.3	5.0	105	16.5	17.8	9.1	156	24.2	24.3	14.7
17		2.6	2.7	1.6	64	8.8	9.5	5.1	106	16.6	18.0	9.2	157	24.3	24.4	14.8
18		2.8	2.9	1.7	65	9.0	9.6	5.2	107	16.8	18.2	9.3	158	24.4	24.5	15.0
19		3.0	3.0	1.8	66	9.2	9.8	5.3	108	16.9	18.3	9.4	160	24.5	24.8	15.1
20		3.2	3.2	1.9	67	9.4	10.0	5.4	109	17.1	18.5	9.5	161	24.6	25.0	15.2
22		3.4	3.4	1.9	68	9.6	10.2	5.5	110	17.2	18.6	10.0	162	24.8	25.1	15.3
23		3.5	3.5	1.9	69	9.7	10.4	5.6	115	18.1	19.6	10.3	157	24.3	24.4	14.8
24		3.7	3.6	2.0	71	10.0	10.9	5.7	116	18.3	19.8	10.5	158	24.4	24.5	15.0
25		3.8	3.7	2.0	72	10.2	11.1	5.8	123	19.3	20.9	10.9	160	24.5	24.8	15.1
26		3.9	3.9	2.1	73	10.4	11.3	5.9	124	19.5	21.1	11.0	161	24.6	25.0	15.2
27		4.2	4.0	2.3	74	10.6	11.6	6.0	126	19.7	21.5	11.4	163	24.9	25.2	15.4
29		4.5	4.2	2.4	75	10.8	11.8	6.1	127	20.1	21.8	11.6	164	25.0	25.2	15.5
30		4.7	4.3	2.5	76	10.9	12.0	6.2	128	20.3	22.1	11.9	165	25.1	25.2	15.7
31	4.8		4.4	2.5	78	11.4	12.5	6.3	129	20.5	22.3	12.0	167	25.2	25.2	15.8
32	5.0		4.6	2.6	79	11.6	12.9	6.4	130	20.8	22.7	12.2	168	25.3	25.3	15.9
33	5.2		4.8	3.0	80	11.8	13.1	6.5	132	20.9	22.8	12.3	169	25.5	25.3	16.0
37	5.7		5.5	3.1	81	11.9	13.2	6.6	133	21.0	22.9	12.4	170	25.6	25.3	16.1
38		5.8	5.8	3.2	82	12.1	13.3	6.7	134	21.2	23.0	12.5	171	25.7	25.3	16.3
39		6.0	5.9	3.3	83	12.3	13.5	6.8	135	21.3	23.2	12.7	174	26.1	25.3	16.4
40		6.1	6.0	3.4	86	12.9	14.1	6.9	136	21.4	23.4	12.9	175	26.3	25.3	16.5
41		6.2	6.1	3.5	87	13.0	14.2	7.0	137	21.6	23.6	13.0	176	26.5	25.3	16.6
44		6.5	6.5	3.6	88	13.2	14.3	7.1	139	21.9	23.7	13.1	177	26.6	25.6	16.8
45		6.6	6.7	3.7	89	13.3	14.4	7.3	140	22.0	23.8	13.2	178	26.7	25.7	17.0
46		6.7	6.8	3.8	90	13.4	14.6	7.5	141	22.2	23.9	13.3	179	26.9	26.0	17.1
47		6.8	6.9	3.9	92	13.8	15.1	7.7	142	22.4	24.0	13.4	181	27.4	26.2	17.2

An accurate OTA has been obtained by the GTA. This work combines between the simulations and the experimental investigations. The excremental work consists of three PV panels installed at 28^o, 30^o, and 50^o TAs. The measurements have been recorded for 181 days. From the recoded data, it can be seen that the 28^o TA has the best performance and the 50 TA has the worst performance. The SR of the 28^o TA is higher than that of the 50^o TA by 59.3% and better than the TA of 30^o by 4.5%. Beside with the experimental work, the GTA and other 8 MHTs have been used to estimate the best values of the OTAs. These MHTs are namely GA, HS, PS, AC, BC, CS, FF, GW, and GTA. All the MHTs have a nearly or even equal OTA and agree with the results obtained from experimental effort. For the same of comparison the OTA for some cities in other countries are computed. The conclusion is that both GTA and the 8 MHTs are very efficient to estimate the OTA.

Contributions: Ashraf K. Abdelaal: Conceptualization, Methodology, Software, Writing- Original draft preparation, Practical measurements. Amira I. A. Alhamahmy: Data curation, Visualization, Software, Investigation, Data Validations, Formal analysis. Hossam El Deen Attia: Software/Coding, Fund, Writing- Reviewing and Editing, Validations of Results of practical setup. Attia A. El-Fergany: Writing- Reviewing and Editing, Supervision, Validations of Results.

Contributions: Ashraf K. Abdelaal: Data curation, Conceptualization, Methodology, Software, Writing- Original draft preparation, Practical measurements, Visualization, Software, Investigation. Attia A. El-Fergany: Formal analysis, Writing-Reviewing and Editing, Supervision, Validations of Results. The authors read and approved the final manuscript.

Data Avaliability Statement: The data that support the findings of this study are available from the corresponding author upon reasonable request.

Conflict of Interest: The authors declare that they have no conflict of interest.

Human and Animal Rights: This article does not contain any studies with animals performed by any of the authors.

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No competing interests reported.

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Maximizing solar radiations of PV panels using artificial gorilla troops reinforced by experimental investigations

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Journal Publication

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Abstract

Figures

1. Introduction

2. Mathematical Model of SR

3. The effect of the TA in the Extra-terrestrial Solar Radiation (SR)

4. Metaheuristic techniques (MHTs)

4.1 Artificial Gorilla Troops Algorithm

4.2 Procedures of the GTA

5. Determination of the OTA by using the GTA

6. Simulation Results and Discussions

7. Performance analysis

7.1 CPU processing time

7.2 Parametric tests

8. Experimental work

8. Conclusions

Declarations

References

Additional Declarations

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\(C=F\times \left(1-\frac{IT}{Max\_IT}\right)\)	(9)
\(F=\text{cos}\left(2\times {r}_{4}\right)+1\)	(10)
\(L=C\times l\)	(11)
\(H=Y*X\left(IT\right)\)	(12)

\(GX\left(k\right)={X}_{silverback}-\left[ {X}_{silverback}Q-X\left(IT\right)Q\right]+X\left(IT\right)]*A\)	(17)
\(Q=2* {r}_{5}-1\)	(18)
\(A= \beta *E\)	(19)
\(E= \left\{\begin{array}{c}{N}_{1} rand \ge 0.5 \\ {N}_{2} rand<0.5 \end{array}\right.\)	(20)